Confocal optical protractor

ABSTRACT

A confocal optical protractor for simultaneously measuring roll angle, pitch angle and yaw angle of an element that includes a tunable laser source generating a laser beam and an SPPR device responsive to the laser beam. The protractor also includes a beam splitter receiving and splitting an output beam from the SPPR device, and a lens being responsive to and projecting the split beam onto the element and being responsive to a reflected beam from the element. The protractor further includes a measurement detector responsive to the reflected beam from the element, where the reflected beam is imaged by the lens onto the measurement detector, and a processor receiving and processing image data from the measurement detector and generating the pitch, yaw and roll angles from the data, where the image data includes an orientation of an vortex intensity pattern in the split beam.

BACKGROUND Field

The present disclosure relates generally to an optical protractor formeasuring roll angle, pitch angle and yaw angle of an element and, moreparticularly, to a confocal optical protractor for simultaneouslymeasuring roll angle, pitch angle and yaw angle of an element, where theprotractor employs a spiral phase plate resonator (SPPR) device thatgenerates an optical vortex pattern beam having intensity peaks that isreflected off of the element and onto a camera or detector.

Discussion

The non-contact measurement of angles, specifically roll, yaw and pitchangles, is often important when manufacturing optical components,building aerospace parts and system level metrology applications,including alignment and tracking, 3D printing, lithography, sample partfabrication, etc. Most approaches in the art that have been used tomeasure angle employ autocollimators, interferometers and mechanicaldevices with movable parts. Roll angle is the most challenging angle tomeasure, and thus, there are a limited number of systems capable ofaccurately measuring roll angle.

Autocollimators have been successful for measuring pitch and yaw angleswith high precision, however, the range over which these angles can bemeasured is limited. Further, in order to measure roll angle, a complexarrangement of autocollimators is required. Interferometers can measurepitch angle and yaw angle, but cannot measure roll angle without acomplex arrangement of additional optical elements, for example,polarization optics and prisms. Further, operation in ruggedenvironments is limited for many free space optics. Mechanical devices,such as mechanical protractors, would require the system to be compact,and be severely limited for non-contact measurement of angle. Further, asystem with movable parts would have a much higher probability offailure during operation over long periods of time.

Roll angles are typically measured by placing the part on a rotatablemount that includes built-in angular ticks along its circumference, andthen rotating the mount to determine the roll angle of the part. Thistechnique usually works well when building small parts, but can bechallenging when fabricating large or very heavy aerospace system parts.Another known roll angle measuring technique includes placing amechanical protractor on the part to determine the angle of interestbetween two fiducials. For this technique, the mechanical protractorwould be in contact with the surface to determine the roll angle, whichcould be detrimental for applications requiring a non-contactmeasurement of the roll angle. In order to measure increasingly smallerangles in confined spaces, the radius of the protractor would have to bemade larger (more angular ticks) or gears would be required on themechanical protractor to amplify the precision of the angle beingmeasured. This could easily increase the size of the mechanicalprotractor for high precision measurements, and thus be problematic whenmeasuring angles in confined spaces. This task becomes even morechallenging when measuring angles on curved surfaces. Furthermore, someapplications in 3D printing, lithography and part fabrication in cleanroom environments require a non-contact determination of roll angle,where the mechanical protractor would be in contact with the part thatis being measured. If the surface is rotating at a constant rate, theroll angle and rotation rate cannot be deduced with a mechanicalprotractor.

Optical systems may provide the ability for making non-contactmeasurements of angle between two static points or lines on a surface,even when the surface is curved and/or rough. In particular, by using acoherent superposition of optical vortices that has a built-incylindrical symmetry, non-contact measurements of angle can be made tovery high accuracy and precision. A property of a coherent superpositionof optical vortices is that it forms a periodic intensity modulation asa function of roll angle (azimuthal angle), which can be projected onthe surface for which the angle is being measured and sensed with adetector.

Various methods exist in the art to create a coherent superposition ofoptical vortices, including methods that use spatial light modulators,spiral phase plates in an interferometer, spiral phase mirrors in aninterferometer, etc. However, these methods do not allow for controllingthe roll angle of the optical vortex without causing a mechanicalrotation of select parts of the optical system that limits theresolution, or the optical system consists of a complex arrangements ofoptical elements including motorized stages, i.e., for the case ofspiral mirrors, q-plates, spiral phase plates, etc. For those methodsthat employ a spatial light modulator (SLM), a computer is required tocontrol the SLM and its resolution and the generation of angulardisplacement is limited by the SLM screen being pixelated and the finiterange of the phase change of the SLM. With these challenges, there is noclear way to miniaturize the system, while maximizing the precision ofthe angle measurement without further complicating the optical systemdesign.

A resonator based on a spiral phase plate, i.e., a spiral phase plateresonator (SPPR) device, is a miniaturized optical element for which acoherent superposition of optical vortices can be generated by eitherreflecting light off of the device or transmitting light through thedevice. There have been fundamental scientific studies showing aresonator effect for a low reflectivity SPPR device. There have alsobeen studies of a rotation sensor based on the rotational Doppler shift.However, there is yet to be a demonstration in the art of a full opticalprotractor system for technological applications, such as manufacturingand production, or determining the roll angle with respect to a fiducialin aerospace systems or otherwise.

U.S. patent application Ser. No. 15/943,240, titled, Optical ProtractorTo Measure Roll Angle On A Static Surface And Rotating Surface, filedApr. 2, 2018, assigned to the assignee of this application and hereinincorporated by reference, discloses an optical protractor that employsa spiral phase plate resonator (SPPR) device for measuring a roll anglebetween two points on a static surface or a rotating surface. Theprotractor includes a tunable laser source that generates a laser beamand an optical component responsive to and converting the laser beam toa single mode laser beam. The SPPR device receives the single mode laserbeam, and includes opposing reflective surfaces that reflect the beamback and forth in the device. One of the reflective surfaces includes aspiral step index that causes multiple reflected beams having differentphases to be combined as an output beam from the device having anoptical vortex intensity pattern, where the intensity pattern includesradial light intensity lines. The protractor includes a lens thatprojects the output beam onto the element, a detector for detectinglight reflected from the element and a processor responsive to signalsfrom the detector. The processor generates images of the reflected lightthat include the optical vortex intensity pattern projected onto theelement, and causes the laser source to change the frequency of thelaser beam so that one of the intensity lines aligns with a first one ofthe points. The processor then causes the laser source to again changethe frequency of the laser beam so that the one intensity line alignswith a second one of the points, where a difference between thefrequencies of the laser beam is used to determine the angle between thepoints.

SUMMARY

The following discussion discloses and describes a confocal opticalprotractor for simultaneously measuring roll angle, pitch angle and yawangle of an element. The protractor includes a tunable laser sourcegenerating a laser beam and a spiral phase plate resonator (SPPR) deviceresponsive to the laser beam. The SPPR device includes opposingreflective surfaces that reflect the laser beam back and forth in thedevice, where one of the reflective surfaces includes a spiral stepindex that causes multiple reflected field amplitudes having differentphases to be combined and generate an optical vortex intensity patterndefined by the phases of the multiple field amplitudes. The intensitypattern from the SPPR device includes a singularity in the middle of thebeam and radial light peaks at different angles about the axis of thebeam. The SPPR device reflects a first beam back towards the lasersource and transmits a second beam away from the laser source. Theprotractor also includes a first beam splitter receiving and splittingeither the first beam or the second beam and generating a splitmeasurement beam, and a lens being responsive to and projecting thefirst split measurement beam onto the element and being responsive to areflected beam from the element. The protractor further includes ameasurement detector responsive to the reflected beam from the element,where the reflected beam is imaged by the lens onto the measurementdetector, and a processor receiving and processing image data from themeasurement detector and generating the pitch, yaw and roll angles fromthe data, wherein the image data includes an orientation of the vortexintensity pattern.

Additional features of the disclosure will become apparent from thefollowing description and appended claims, taken in conjunction with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram of a confocal optical protractor formeasuring roll, pitch and yaw angles of an element, where a measurementbeam is reflected from a spiral phase plate resonator (SPPR) device andthen reflected off of the element;

FIG. 2 is an isometric view of the SPPR device separated from theoptical protractor shown in FIG. 1;

FIG. 3 is an side view of the SPPR device showing a beam being reflectedtherein;

FIG. 4 is an illustration of a single pixel detector array includingeight single pixel detectors arranged in a circle;

FIG. 5 is an optical vortex intensity profile image of the beamreflected from the SPPR device in the protractor shown in FIG. 1;

FIG. 6 is an optical vortex intensity profile image of a reference beamtransmitted through the SPPR device in the protractor shown in FIG. 1;

FIGS. 7 and 8 are the optical vortex intensity profile image shown inFIG. 5 with the beam reflected above and below the center point,respectively, for measuring pitch angle;

FIGS. 9 and 10 are the optical vortex intensity profile image shown inFIG. 5 with the beam moved to the left side and the right side,respectively, for measuring yaw angle;

FIGS. 11 and 12 are the optical vortex intensity profile image shown inFIG. 5 with the beam rotated clockwise and counter-clockwise,respectively, for measuring roll angle;

FIG. 13 is a schematic block diagram of a confocal optical protractorfor measuring roll, pitch and yaw angles of an element, where ameasurement beam is transmitted through an SPPR device;

FIG. 14 is an optical vortex intensity profile image showing a beamtransmitted through the SPPR device in the protractor shown in FIG. 13;

FIGS. 15 and 16 are the optical vortex intensity profile image shown inFIG. 14 with the beam reflected above and below the center point,respectively, for measuring pitch angle;

FIGS. 17 and 18 are the optical vortex intensity profile image shown inFIG. 14 with the beam moved to the left side and the right side,respectively, for measuring yaw angle;

FIGS. 19 and 20 are the optical vortex intensity profile image shown inFIG. 14 with the beam rotated clockwise and counter-clockwise,respectively, for measuring roll angle;

FIG. 21 is a flow chart diagram showing a process for finding a beamcentroid for an optical vortex intensity profile image having highcontrast fringes;

FIG. 22 is a flow chart diagram showing a process for finding a beamcentroid for an optical vortex intensity profile image having lowcontrast fringes;

FIG. 23 is a flow chart diagram showing a process for determining pitchangle and yaw angle; and

FIG. 24 is a flow chart diagram showing a process for determining rollangle.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The following discussion of the embodiments of the disclosure directedto a confocal optical protractor including an SPPR device for measuringroll, pitch and yaw angles of an element is merely exemplary in natureand is in no way intended to limit the disclosure or its applications oruses.

As will be discussed in detail below, the present disclosure describesan optical system, or optical protractor, that provides an “all optical”process with no moving parts for measuring the roll, pitch and yawangles of an element. The optical system has application for themanufacture and production of various components and parts, such as forunmanned aerial vehicles, planes, aircraft carriers, ballistic missiles,etc., where a non-contact measurement of pitch, yaw and roll angles of apart is important. The optical system also has machine visionapplications, such as in robots and autonomous vehicles, to determinethese angles during pattern recognition.

The main element of the optical system is a spiral phase plate resonator(SPPR) device in which a light beam at a certain frequency undergoesmultiple reflected round trips within the device to create an outputbeam having an angular intensity modulation interference pattern as afunction of beam angle. Precise changes of the wavelength of the beamentering the SPPR device rotate angular intensity peaks in the patternof the beam output from the SPPR device that when projected onto astatic surface can be detected to measure the pitch, yaw and rollangles. The intensity modulation interference pattern in the output beamis the result of a coherent superposition of select optical vortexwinding numbers emerging from the SPPR device.

To ensure high accuracy of the angles being measured even under harshenvironments, such as the presence of vibrations and temperaturegradients, a method for calibrating the optical system is necessary. Themethod includes calibrating the rotation angle of the optical vortexintensity pattern to the wavelength of the beam, and monitoring theangular displacement of the optical intensity pattern on a detector,such as a CCD camera, with a reference beam. Any spurious changes in theoptical system, such as changes in the wavelength of the beam from thelaser source, changes in refractive index of the optics, or vibrationsof the surface that is being measured, can be compensated duringmeasurement of the angles. The images from the CCD camera are read inreal time using image processing algorithms that have reduced errorswhen finding the center of optical vortices and other forms ofsystematic errors in the determination of the angles. The frequency ofthe input beam to the SPPR device is locked and varied using standardtechniques, such as phase locking schemes, amplitude locking schemes,etc., and increments of the frequency would rotate the intensity patternfor measurement, calibration and real time monitoring.

FIG. 1 is a schematic block diagram of an optical system 10 of the typediscussed above for simultaneously measuring the roll, pitch and yawangles between fiducial lines on a static or rotating surface, anddetermining the rotation rate of the rotating surface. The system 10includes a narrow linewidth laser source 12 that is tunable, and thatemits a coherent laser beam, for example, in the visible-IR frequencyrange, into a single mode optical fiber 14 that provides a laser beam 18in, for example, the TEM₀₀ Gaussian mode. In an alternate embodiment,other optical elements instead of the single mode optical fiber 14 canbe employed to provide the TEM₀₀ Gaussian mode. For example, anappropriately designed aperture (not shown) could be used to put thebeam 18 in the TEM₀₀ Gaussian mode or clean up the optical mode. Thebeam 18 emitted from the fiber 14 is collimated by a collimator 16positioned at the end of the fiber 14 to ensure that the beam 18propagates through the entire optical system 10 with minimal divergence.Light reflected back into the laser source 12 may cause beam jitter inthe laser cavity causing intensity fluctuations of the output laser beam18 or spurious frequency shifts in the laser wavelength, which couldcause instability of the modes in the laser cavity and cause the lasersource 12 to go out of lock. Therefore, an optical isolator 20 ispositioned after the output of the collimator 16 to prevent backreflection of the laser beam 18 into the laser source 12.

The single mode beam 18 that propagates through the optical isolator 20is split by a beam splitter 22 where a small portion of the beam 18 issent to a fast detector 24 that monitors beam intensity and theremaining portion of the beam 18 is sent to an SPPR device 26, where itis reflected back and forth in the device 26 as a result of its finitereflectivity. FIG. 2 is an isometric view and FIG. 3 is a side view ofthe device 26 separated from the system 10. The device 26 includes anoptically transparent block 28, such as glass, having a reflective plate30, such as a smooth reflective material coating, on an input side ofthe block 28 that is optically transmissive enough to allow the beam 18from the collimator 16 to propagate into the block 28. The device 26also includes a step-wise spiral reflector 32, such as a polymer orglass layer having a reflective material coating, with an azimuthallyvarying step 34 having height Δh on an output side of the block 28 thatis also optically transmissive enough so that an output beam canpropagate therethrough and be output from the device 26. Although smoothreflective material coatings are employed in this design to providereflective surfaces on the block 28, in alternate designs nanoscalestructures can be used to provide the reflectivity of the beam 18 in theblock 28.

If the beam 18 propagated through the block 28 with no surfacereflectivity, an optical vortex beam with a well-defined winding numberwould be produced on the output plane of the device 26, where the device26 would act as a spiral phase plate. By providing finite reflectivityon opposing surfaces of the device 26 and providing the reflector 32having the gradually varying azimuthal thickness, the device 26 operatesas a spiral phase plate resonator (SPPR), where an optical vortex beamis output from the device 26 as a coherent superposition of opticalvortices separated by specific positive winding numbers. In other words,each reflection of the beam 18 within the device 26 creates anindividual optical vortex beam having a unique phase that is output fromthe device 26, shown as amplitudes U₁-U_(N), each having a differentwinding number, i.e., orbital angular momentum, where the beam is asuperposition of all of the optical vortex amplitudes U₁-U_(N) withdifferent winding numbers having different orbital angular momentumstates, and is referred to herein as an optical vortex intensitypattern. The optical vortex intensity pattern is thus a periodicintensity interference pattern based on the phase of the beams U₁-U_(N)that varies as a function of the angle of the vortex beam, where therotation of the intensity pattern is controlled by the frequency of thebeam 18.

The optical vortex intensity pattern of the beam 18 is both output fromthe input side of the SPPR device 26 towards the beam splitter 22 as areflected measurement beam 40 and is output from the output side of theSPPR device 26 as a transmitted reference beam 42 that is used forcalibration purposes. In this non-limiting embodiment, the SPPR device26 is a commercial-off-the-shelf (COTS) device having an internalreflectivity of about 0.04. This reflectivity causes the vortexintensity peaks in the measurement beam 40 to be of high contrast andthe vortex intensity peaks in the transmitted reference beam 42 to be oflow contrast. By using the reflected beam 40 for the angle measurements,the more distinct peaks allow background light to be more easilyremoved.

The reference beam 42 is imaged by a lens 50 positioned at two focallengths from the SPPR device 26 onto a charge coupled device (CCD)camera 54 through an attenuator 56, and provides a reference of the beamorientation for roll angle calculations. The measurement beam 40 isreflected by the beam splitter 22 towards a second beam splitter 60 thatdirects a small portion of the measurement beam 40 to a detector 62 thatkeeps track of the orientation of the optical vortex measurement beam 40and the intensity of the beam 40 reflected from the SPPR device 26. Thedetector 62 is shown as a multiple pixel detector, such as a CCD camera,but could be any detector suitable for the purposes discussed here. Forexample, the detector 62 could be a single pixel detector array 76including eight single pixel detectors 78 arranged in a circle ring, asshown in FIG. 4. The circular ring could allow for measuring therotational displacement of the beam 40 to high precision.

The main portion of the measurement beam 40 is imaged by a lens 64, or aseries of lenses, onto a platform 66 through a shutter 68, where thelens 64 collimates the beam 40 to image the platform 66 in a confocalimaging geometry. The reflected beam from the platform 66 is directed bythe beam splitter 60 to a CCD camera 70 that provides the anglemeasurements, where the lens 64 images the reflected beam on the camera.A narrowband filter 72 positioned in front of the camera 70 reduces thesources of background light at other wavelengths. Further, the lens 64will reduce the field-of-view (FOV) of the camera 70, which also willreduce the amount of backscattered light entering the camera 70. Whenthe shutter 68 is closed, the beam 40 is reflected onto the camera 70through the beam splitter 60. When the shutter 68 is open, the beam 40goes through the shutter 68 and is retro-reflected from the platform 66onto the camera 70. The CCD camera 70 also serves to calibrate theinitial position of the beam 40.

An x-y-z coordinate system is illustrated relative to the platform 66,where rotation about the x-axis indicates yaw angle, rotation about they-axis indicates pitch angle and rotation about the z-axis indicatesroll angle. An optical vortex intensity profile of the measurement beam40 having high contrast fringes as imaged on the camera 70 isillustrated in FIG. 5, where the device 26 is a low internalreflectivity SPPR device, such as |r₂|²=0.04. An optical vortexintensity profile of the reference beam 42 having low contrast fringesas imaged on the camera 54 is illustrated in FIG. 6. In theseillustrations, the shaded areas represent the vortex intensity peaks.The system 10 works well when a higher internal reflectivity device isimplemented in this embodiment, and the SPPR device 26 could be facingin the forward direction or in the reverse direction.

The system 10 is calibrated in the same manner discussed above using thecamera 54 for an accurate determination of the angles. From thismeasurement, a transfer function that effectively defines thecalibration function of the optical system 10 is obtained. The transferfunction converts a change in laser frequency to a change in angle, evenin the presence of thermal effects of the elements in the optical system10. Ideally, materials with a low coefficient of thermal expansion wouldbe used in the optical system 10 for high precision measurements.Nevertheless, the camera updates from the calibration process before orduring measurements enables angle determination on a static surface,even in the presence of thermal effects and vibrations. For measurementsperformed after the focus of the beam 42, the Gouy phase will cause anadditional shift in the rotation of the reference beam 42. This effectis easily taken into account during the calibration of the opticalsystem 10.

The system 10 allows the optical vortex beam to remain collimated overlong distances for the purposes of illuminating the platform 66. Todetermine the roll angle, the frequency of the beam 18 is shifted torotate the angular intensity profile. To measure the pitch angle and theyaw angle, the centroid of the beam 40 is moved from one point toanother. A distance measuring device, such as LiDAR, RADAR, etc., can beused to estimate distance when measuring yaw angle and pitch angle.

A processor 74 controls the system 10 and receives signals from thecameras 54 and 70 and the detector 62, and tunes the laser source 12, todetermine the measurements of roll, yaw and pitch angles consistent withthe discussion herein. As will be discussed in further detail below, thebeam 40 is reflected from the platform 66 when it is in a referenceposition to determine the distance between the platform 66 and camera 70and identify an initial beam profile. A shift in the beam profile aboveor below the center point of the initial beam profile along the y-axisin the described orientation is a measure of the pitch angle as shown bythe optical vortex intensity profile images in FIGS. 7 and 8. Further, ashift in the beam profile to the left or right of the center point ofthe initial beam profile along the x-axis in the described orientationis a measure of the yaw angle as shown by the optical vortex intensityprofile images in FIGS. 9 and 10. It is noted that the distance to theplatform 66 and a shift of the beam 40 on the camera 70 is used tomeasure the pitch and yaw angles. The beam 40 is rotated clockwise orcounter-clockwise relative to a fiducial (not shown) on the platform 66to measure the roll angle as shown by the optical vortex intensityprofile images in FIGS. 11 and 12.

In the system 10, the measurement beam 40 used to measure the pitch, yawand roll angles was reflected from the SPPR device 26 because the device26 has a low internal reflectivity, as discussed. In an alternateembodiment, the SPPR device 26 can be replaced with a mid-range internalreflectivity device, such as |r₂|²=0.57, where the beam transmittedthrough the device is the measurement beam. FIG. 13 is a schematic blockdiagram of an optical system 80 of this type for simultaneouslymeasuring roll, pitch and yaw angles, where like elements to the system10 are identified by the same reference number. In this embodiment, theSPPR device 26 is replaced with an SPPR device 82, which is a customdevice having a high internal reflectivity, the detector 24 and the beamsplitter 22 are eliminated, and a beam splitter 84 is provideddownstream of the SPPR device 82, where the vortex beam from the device82 is split into the reference beam 42 and the measurement beam 40.

The transmitted beam optical intensity profile through the SPPR device82 is illustrated in FIG. 14. In the same manner as discussed above forthe system 10, the beam 40 is reflected from the platform 66 when it isin a reference position to determine the distance between the platform66 and camera 70 and identify an initial beam profile. A shift in thebeam profile above or below the center point of the initial beam profilealong the y-axis in the described orientation is a measure of the pitchangle as shown by the optical vortex intensity profile images in FIGS.15 and 16. Further, a shift in the beam profile above or below thecenter point of the initial beam profile along the x-axis in thedescribed orientation is a measure of the yaw angle as shown by theoptical vortex intensity profile images in FIGS. 17 and 18. Again, it isthe distance to the platform 66 and a shift of the beam 40 on the camera70 that are to measure the pitch and yaw angles. The beam 40 is rotatedclockwise or counter-clockwise relative to a fiducial (not shown) on theplatform 66 to measure the roll angle as shown by the optical vortexintensity profile images in FIGS. 19 and 20.

A COTS SPPR device with low reflectivity at its surfaces or a customfabricated SPPR device with high reflectivity at its surfaces can beused in the confocal optical protractor (COP) for the systems 10 and 80,as described. For a COTS SPPR device, the reflectivity at the surfacesof the device is relatively low, i.e., |r₂|²˜|0.219|²=0.047. Thus, therewill be approximately two-thirds less photon counts making rotationalmeasurements compared to the maximum number of photons that can bemaking rotational position measurements on the internal surface of thecamera 70, and on the platform 66 of interest. Depending on the albedoof the platform 66, there may be even fewer light particles imaged ontothe camera 70. One of the key advantages of this confocal geometry ofthe optical protractor is the presence of high contrast fringes (unity)regardless of the reflectivity of the SPPR device. This allows forbetter signal to noise ratio, especially for a COTS SPPR device. Whenthe reflectivity of the SPPR device is increased to a value of|r₂|²=|0.577|²=0.33, then the maximum number of light particles will bemaking rotational position measurements in the transmission geometry ofthe SPPR device for increased signal to noise ratio on the camera 70.

The equations describing the transmission amplitude through the SPPRdevice 26, and reflection amplitude from the SPPR device 26, can bederived using a matrix formalism. For the purpose of clarity andsimplicity, the transmission through the SPPR device 26 or 82 isrepresented as:T[ϕ]=B+A*T ₁[ϕ,ϕ₀ ,r ₂,β],  (1)where A, Band ϕ₀ are used to estimate the amplitude, estimate thebackground, and track the rotation of the angular intensity patternsignal with the fit routines, T₁[ϕ,ϕ₀,r₂,β] is the normalizedtransmission function that constitutes the angular position ϕ₀ of anSPPR with a Fresnel reflection coefficient r₂, and the number ofazimuthally varying intensity peaks β. The parameters r₂ and β are knownparameters when the system 10 is constructed and does not change duringsystem operation. The reflectivity of the SPPR device 26 or 82 isdefined as |r₂|².

Similarly, the reflection from the SPPR device 26 is represented as:R[ϕ]=B+A*R ₁[ϕ,ϕ₀ ,r ₂,β],  (2)where R₁[ϕ,ϕ₀,r₂,β] is a normalized reflection function.

The roll angle, pitch angle and yaw angle are measured by keeping trackof specific properties of the optical vortex beam retro-reflected fromthe external surface onto the camera 70. These properties include thecentroid of the individual intensity peaks, the centroid of the wholeoptical vortex beam and the rotational displacement of the opticalvortex intensity profile. There will be four intensity peaks projectedonto the surface of the platform 66 for which the angles are to bemeasured. The algorithms for measuring the roll, pitch and yaw angleswill enable the position of the individual intensity peaks and thecenter of the optical vortex to be known to a high degree of accuracyand precision. Due to the four separate intensity peaks, the measurementprecision is improved by a factor of four in the measure of the rollangle, pitch angle, and roll angle, compared to if one narrow intensitypeak was used to determine the angle. While this design uses fourintensity peaks, there could be significantly more intensity peaks orless intensity peaks emerging from the SPPR device 26.

The roll angle is determined by keeping track of the rotation of theoptical vortices, i.e., the rotational displacement (angulardisplacement) of the optical vortex beam on the camera 70. Theresolution in the determination of roll angle is quite high, whilemaintaining a large range over which the roll angle is measured. Thisangle can be extended over the 360° measurement range. The pitch angleis determined by keeping track of the vertical displacement of theoptical vortex beam centroid from the external platform on the camera70. Similarly, the yaw angle is determined by keeping track of thehorizontal displacement of the retro-reflected optical vortex beam fromthe external platform. The yaw angle and pitch angle are computed fromboth the distance to the target and the displacement of the beam on thecamera 70. Before the optical vortex beam is retro-reflected from theplatform 66, it is internally retro-reflected off the shutter 68 whenthe shutter 68 is closed to determine the initial position of theoptical vortex beam 40. This includes the initial position of the beamcentroid, and the initial position of the angular intensity peaks. Thisprocess occurs in sequence with the other system calibration processesincluding laser intensity using the detector 24 and laser frequencycalibration using the camera 54, as well as monitoring the internalrotation of the optical vortex beam 48 on the cameras 54 and 70 and thedetector 62. In a different embodiment, the initial position could bedetermined on an external planar surface of known angle for the initialangle calibration. Furthermore, there is a stored transfer functionwhich converts the laser wavelength to rotation of the optical vortexbeam.

The angular displacement to measure the roll angle and the displacementsto estimate the yaw angle and the pitch angle are estimated fromnon-linear fitting routines. The yaw angle and the pitch angle aredetermined from a vertical and horizontal displacement in the centroidof the four intensity peaks, on the x axis and y axis of the camera 70,respectively, as well as distance to the target. The roll angle isdetermined by the rotational displacement of the intensity peaks. Asthere are four individual intensity peaks projected onto the camera 70with unity contrast, these intensity peaks are fitted individually. Fromthe position of the intensity peaks, the centroid of the entire beam isobtained. The centroids are first calculated from the data using theappropriate formula, and then these values are used as initial values inthe non-linear fitting routine to track the position of interest. Theprecise determination of the beam centroid is the first step indetermining the angular displacement of the retro-reflected beam. In theevent that there is speckle in the images, then multiple images could beaveraged together to reduce the effects of speckle.

The determination of the roll, pitch and yaw angles requires knowledgeof the absolute center of the beam 40. For an optical vortex beam with asingularity, i.e., a very small optical vortex core (or no core)generated by the SPPR device 26, the center of the beam 40 is defined asthe point where all of the intensity peaks come together, which isequivalent to the beam's centroid. An algorithm for computing the centerof the beam 40 is discussed below. The algorithm works well for an evennumber of optical vortex intensity peaks, i.e., when β is an evennumber, and thus for this purpose, it is assumed that β=4. Nevertheless,the algorithm could be adapted to work well for an odd number ofintensity peaks. The algorithm is discussed for two cases, namely, afirst case for an optical vortex intensity profile having high contrastfringes of the beam 40 imaged on the camera 70, and a second case for anoptical vortex intensity profile having low contrast fringes of the beam40 imaged on the camera 70. More particularly, depending on the choiceof the SPPR device 26 or 82, the camera 70 could receive high or lowcontrast fringes. When the SPPR device has low reflectivity, then thecamera 70 produces images having low contrast fringes, but with a mid tohigh reflectivity SPPR device, i.e., a custom SPPR device, the camera 70produces images having high contrast fringes. The camera 70 will alwayshave relatively high contrast fringes for the systems 10 and 80.

FIG. 21 is a flow chart diagram 90 showing a process for determining thecenter of the optical vortex intensity profile having high contrastfringes of the beam 40 imaged on the camera 70. The shutter 68 is closedat box 92 so that there is no light from the external surfaces, althoughit may not be necessary in some designs to close the shutter 68. Whenthe shutter 68 is closed, the beam 40 is retro-reflected off of theshutter 68 onto the camera 70 at box 94. The pixel screen on the camera70 is segmented into a number of quadrants representative of the numberof intensity peaks in the beam 40 at box 96. In this example, there arefour intensity peaks, i.e., β=4, and thus, four quadrants, where eachquadrant is integrated on the x-axis and the y-axis at box 98. Thecentroid and the width of the intensity peak in each quadrant areestimated using the collected data at box 100, and these values arestored individually for all four of the quadrants. A non-linear fittingroutine is applied to the intensity peak in each quadrant at box 102,where the initial values in the fitting routine are estimated at the box100, and where a Gaussian-like function is employed as the model in thefitting routine in one non-limiting embodiment. The x and y centroidposition and width of each intensity peak is estimated using the fitroutine at box 106. From the values of the centroid position of eachintensity peak, the center position of the beam 40 is computed tosub-pixel accuracy, and the values are stored at box 108. One way ofcomputing the center position of the beam 40 is by taking the average ofthe respective x and y intensity peaks in diagonal quadrants. The valuesof the centroid and width of the individual intensity peaks in eachquadrant, and the centroid of the entire beam forms the initial positionin the determination of angle when the shutter 68 is closed or open.

The low fringe contrast is for the case of optical transmission throughan SPPR when the reflectivity of the SPPR device 26 is low. This wouldbe the case for the optical hardware in the system 10, where theimage/frame is typically monitored on the camera 54 during dynamiccalibration. Finding the center of the optical vortex beam 40 isgenerally done when the system 10 is initially built. The center pointis then monitored using this procedure to ensure that there is nostatistically significant deviation in the center position during thesystem operation.

FIG. 22 is a flow chart diagram 112 showing a process for determiningthe center of the optical vortex intensity profile having low contrastfringes of the beam 42 imaged on the camera 54. The beam 42 istransmitted through the SPPR device 26 at box 114, and the integratedcounts on the x axis and y axis are computed at box 116. The centroidand width of the beam 42 are estimated at box 118 using the collecteddata, and these values are stored. A non-linear fitting routine isapplied to the beam 42 at box 102, where the initial values in thefitting routine are estimated at the box 118, and where a Gaussian-likefunction is employed as the model in the fitting routine for the wholebeam 42 in one non-limiting embodiment. The x and y centroid positionand the width of the beam 42 are obtained from the non-linear fittingroutine at box 124. The operations at boxes 116 to 124 are repeated atdifferent rotation angles by varying the laser frequency of the beam 42to ensure the consistency of the beam center (centroid) position at box126. In the case when a low reflectivity SPPR device is used, this valueis compared to the previously stored value of the center position of thebeam 42 at box 128. There should not be much deviation from the storedvalues during the initial calibration. In other words, the deviationshould not be more than subpixel values.

FIG. 23 is a flow chart diagram 130 showing a process for computing thepitch and yaw angles of the platform 66. The shutter 68 is closed at box132 so that there is no light from the external surface onto the camera70. The beam 40 is retro-reflected from the shutter 68 (or externalcalibration surface) and into the camera 70 at box 134. The centroid ofthe beam 40 is computed as discussed above in the flow chart diagrams 90or 112 at box 136. The shutter 68 is opened at box 138, and the centroidof the retro-reflected beam is computed at box 140. The pitch angle isdetermined from the vertical displacement of the beam 40 on the camera70 at box 142, where each value of vertical displacement corresponds toa measure of the pitch angle. The yaw angle is determined from thehorizontal displacement on the camera 70 at box 144, where each value ofthe horizontal displacement corresponds to a yaw angle. If the pitchangle and the yaw angle are continuously changing, then continuousmeasurements can be performed to estimate the changing angle as afunction of the position on the screen of the camera 70 at box 146. Thepitch and yaw angles are stored at box 148.

FIG. 24 is a flow chart diagram 150 showing a process for computing theroll angle of the platform 66. The shutter 68 is closed at box 152 sothat no light is incident on the platform 66. The intensity of the lasersource 12 is stabilized using the detectors 24 and 62 and the camera 54at box 154, and the initial frequency of the laser source 12 isdetermined by the angular position of the intensity peak on the cameras54 and 70 at box 156. The cameras 54 and 70 are synchronized at box 158to ensure that they receive the image frames simultaneously. Thecentroid of the beam 40 on the cameras 54 and 70 are estimated asdescribed in the flow diagram 90 or 112 at box 160. The presence ofbackground is subtracted from the values obtained by the non-linearfitting routine. The centroid of the beam 40 that is retro-reflectedfrom the shutter 68 onto the camera 70 is estimated at box 162. Theintegrated counts along the radial direction starting from the beamcentroid position are computed as a function of the roll angle on thecamera 54 at box 164, and the positions of the angular intensity peaksusing a non-linear fitting routine are estimated at box 166, where thesevalues are stored. The integrated counts along the radial directionstarting from the beam centroid position are computed as a function ofthe roll angle on the camera 70 at box 168, and the positions of theangular intensity peaks using a non-linear fitting routine are estimatedat box 170, where these values are stored.

The shutter 68 is opened at box 172, and the beam 40 is projected ontothe platform 66 and is imaged on the camera 70 at box 174. The centroidof the beam 40 imaged on the platform 66 is determined using the flowchart diagram 90 or 112 at box 176. The radially integrated countsstarting from the centroid of the beam 40 are computed as a function ofthe roll angle at box 178. The position of the intensity peaks areobtained from the non-linear optimization fitting routine at box 180.The initial positioning of the intensity peaks for the non-linearfitting routine are stored from the calibration process, where the beam40 is retro-reflected from the shutter 68, at box 182. When the platform66 is rotated, the optical vortex beam tracks the rotation through achange in the laser beam frequency, which rotates the orientation of theoptical vortex intensity profile. The roll angle is estimated at box184. If the platform 66 is rotated in incremental steps, then theoptical vortex pattern of the beam 40 can be rotated in incrementalsteps to determine the roll angle. If there is smooth continuousrotation of the platform 66 at a fast rate, then the roll angle can beobtained using the rotational Doppler shift.

The foregoing discussion discloses and describes merely exemplaryembodiments of the present disclosure. One skilled in the art willreadily recognize from such discussion and from the accompanyingdrawings and claims that various changes, modifications and variationscan be made therein without departing from the spirit and scope of thedisclosure as defined in the following claims.

What is claimed is:
 1. An optical system for measuring pitch, yaw androll angles of an element, said system comprising: a tunable lasersource generating a laser beam; a spiral phase plate resonator (SPPR)device responsive to the laser beam, said SPPR device including opposingreflective surfaces that reflect the laser beam back and forth in thedevice, wherein one of the reflective surfaces includes a spiral stepindex that causes multiple reflected amplitudes having different phasesto be combined and generate an optical vortex intensity pattern definedby the phases of the multiple amplitudes, where the intensity patternincludes a singularity and radial light peaks, said SPPR devicereflecting a first beam back towards the laser source and transmitting asecond beam away from the laser source; a first beam splitter receivingand splitting either the first beam or the second beam and generating asplit measurement beam; a lens being responsive to and projecting thefirst split measurement beam onto the element and being responsive to areflected beam from the element; a measurement detector responsive tothe reflected beam from the element, where the reflected beam is imagedby the lens onto the measurement detector; and a processor receiving andprocessing image data from the measurement detector and generating thepitch, yaw and roll angles from the data, wherein the image dataincludes an orientation of the vortex intensity pattern.
 2. The opticalsystem according to claim 1 wherein the vortex intensity patternincludes one intensity peak in each of four quadrants.
 3. The opticalsystem according to claim 1 wherein the pitch angle is determined by ashift of the vortex intensity pattern in one plane, the yaw angle isdetermined by a shift of the vortex intensity pattern in another planeorthogonal to the one plane, and the roll angle is determined by arotation of the vortex intensity pattern.
 4. The optical systemaccording to claim 1 further comprising a second beam splitter receivingand directing the split measurement beam to the lens, wherein the secondbeam splitter receives and directs the reflected beam to the measurementdetector.
 5. The optical system according to claim 4 further comprisinga shutter through which the split measurement beam propagates from thelens to the element.
 6. The optical system according to claim 5 furthercomprising a detector that is responsive to a split reflected beam fromthe second beam splitter when the shutter is closed, said detectorkeeping track of the orientation of the reflected beam and the intensityof the first or second beam.
 7. The optical system according to claim 6wherein the detector is a multiple pixel detector or a single pixeldetector array including multiple single pixel detectors arrange in acircle.
 8. The optical system according to claim 1 wherein the SPPRdevice is a low reflectivity device and the first beam splitter receivesthe first beam.
 9. The optical system according to claim 8 furthercomprising an intensity detector responsive to a split beam from thefirst beam splitter, said intensity detector monitoring beam intensity.10. The optical system according to claim 8 wherein the reflectivity ofthe SPPR device is about 0.04.
 11. The optical system according to claim1 wherein the SPPR device is a high reflectivity device and the firstbeam splitter receives the second beam.
 12. The optical system accordingto claim 11 wherein the reflectivity of the device is about 0.5.
 13. Theoptical system according to claim 1 wherein the SPPR device generates areference beam transmitted through the SPPR device, said reference beambeing projected onto a calibration detector for generating a referenceorientation of the vortex intensity pattern.
 14. The optical systemaccording to claim 13 wherein the measurement and calibration detectorsare CCD cameras.
 15. An optical system for measuring pitch, yaw and rollangles of an element, said system comprising: a tunable laser sourcegenerating a laser beam; a spiral phase plate resonator (SPPR) deviceresponsive to the laser beam, said SPPR device including opposingreflective surfaces that reflect the laser beam back and forth in thedevice, wherein one of the reflective surfaces includes a spiral stepindex that causes multiple reflected amplitudes having different phasesto be combined and generate an optical vortex intensity pattern definedby the phases of the multiple amplitudes, where the intensity patternincludes a singularity and radial light peaks, said SPPR devicereflecting a first beam back towards the laser source and transmitting asecond beam away from the laser source; a calibration detectorresponsive to the second beam and generating a reference orientation ofthe vortex intensity pattern; a first beam splitter receiving andsplitting the first beam and generating a split measurement beam; a lensbeing responsive to and projecting the first split measurement beam ontothe element and being responsive to a reflected beam from the element; ameasurement detector responsive to the reflected beam from the element,where the reflected beam is imaged by the lens onto the measurementdetector; and a processor receiving and processing image data from themeasurement detector and the reference orientation of the vortexintensity pattern and generating the pitch, yaw and roll angles from thedata, wherein the image data includes an orientation of the vortexintensity pattern, and wherein the pitch angle is determined by a shiftof the vortex intensity pattern in one plane, the yaw angle isdetermined by a shift of the vortex intensity pattern in another planeorthogonal to the one plane, and the roll angle is determined by arotation of the vortex intensity pattern.
 16. The optical systemaccording to claim 15 wherein the vortex intensity pattern includes oneintensity peak in each of four quadrants.
 17. The optical systemaccording to claim 15 further comprising a second beam splitterreceiving and directing the split measurement beam to the lens, whereinthe second beam splitter receives and directs the reflected beam to themeasurement detector.
 18. The optical system according to claim 17further comprising a shutter through which the split measurement beampropagates from the lens to the element.
 19. The optical systemaccording to claim 18 further comprising a detector that is responsiveto a split reflected beam from the second beam splitter when the shutteris closed, said detector providing beam calibration.
 20. The opticalsystem according to claim 15 further comprising an intensity detectorresponsive to a split beam from the first beam splitter, said intensitydetector monitoring beam intensity.
 21. An optical system for measuringpitch, yaw and roll angles of an element, said system comprising: atunable laser source generating a laser beam; a spiral phase plateresonator (SPPR) device responsive to the laser beam, said SPPR deviceincluding opposing reflective surfaces that reflect the laser beam backand forth in the device, wherein one of the reflective surfaces includesa spiral step index that causes multiple reflected amplitudes havingdifferent phases to be combined and generate an optical vortex intensitypattern defined by the phases of the multiple amplitudes, where theintensity pattern includes a singularity and radial light peaks, saidSPPR device outputting a vortex beam; a beam splitter receiving andsplitting the vortex beam into a measurement beam and a calibrationbeam; a calibration detector responsive to the calibration beam andgenerating a reference orientation of the vortex intensity pattern; alens being responsive to and projecting the measurement beam onto theelement and being responsive to a reflected beam from the element; ameasurement detector responsive to the reflected beam from the element,where the reflected beam is imaged by the lens onto the measurementdetector; and a processor receiving and processing image data from themeasurement detector and the reference orientation of the vortexintensity pattern and generating the pitch, yaw and roll angles from thedata, wherein the image data includes an orientation of the vortexintensity pattern, and wherein the pitch angle is determined by a shiftof the vortex intensity pattern in one plane, the yaw angle isdetermined by a shift of the vortex intensity pattern in another planeorthogonal to the one plane, and the roll angle is determined by arotation of the vortex intensity pattern.